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Simple piecewise geodesic interpolation of simple and Jordan curves with applications

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Boedihardjo, Horatio and Geng, Xi (2014) Simple piecewise geodesic interpolation of simple and Jordan curves with applications. Constructive Approximation, 42 (1). pp. 161-180. doi:10.1007/s00365-014-9257-z

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Official URL: https://doi.org/10.1007/s00365-014-9257-z

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Abstract

We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green’s theorem and the uniqueness of signature for planar Jordan curves with finite p -variation for 1⩽p<2.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Journal or Publication Title: Constructive Approximation
Publisher: Springer
ISSN: 1432-0940
Official Date: 13 August 2014
Dates:
DateEvent
13 August 2014Published
3 June 2014Accepted
Volume: 42
Number: 1
Page Range: pp. 161-180
DOI: 10.1007/s00365-014-9257-z
Status: Peer Reviewed
Publication Status: Published
Funder: European Research Council
Grant number: 291244
Open Access Version:
  • ArXiv

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